England’s shortage of affordable rented housing shows no sign of ending, as official figures revealed on Wednesday that only 37,825 new homes were built to be let at discounted rents last year, despite a national housing waiting list of more than 1.1 million households.

The number of new homes classed as social housing and available at the cheapest rents from councils remained historically low at a mere 6,287, the second-lowest level in peacetime since council house building began in earnest in 1921.

The shortfall in new affordable homes is likely to fuel householders’ reliance on the private rental market. New research also published on Wednesday showed such housing is almost completely unaffordable in many areas for people who rely on housing benefit, which has been frozen since 2016.

In a third of areas of England fewer than 10% of homes are now affordable to welfare recipients, according to a study by the Chartered Institute of Housing and the homelessness charity Crisis. That meant increasing numbers of people were being pushed into homelessness or forced to live in emergency or temporary accommodation, the charity said.

Ministers last month celebrated increases in overall housebuilding to a rate of more than 200,000 a year, although that remains short of the 250,000-a-year target set in the Conservatives’ 2017 general election manifesto. The large majority of the completions were homes for sale. The number of new homes which the government classes as affordable was 57,485 in 2018-19, a figure surpassed four times in the last decade.

The fastest rising subset of those “affordable homes” was shared ownership housing which involves tenants buying part of the property. The number of these properties completed increased from 11,084 to 17,024.

Housing campaigners are urging all parties to tackle the housing crisis in their election manifestos, with Labour’s due to be published on Thursday. They warn that the lack of new council and housing association properties is forcing families who cannot afford to buy to rely on private tenancies, which remain vulnerable to no-fault evictions and widespread problems with building standards. With more than 4.5 million households in England renting privately and a doubling of the number of families in rented homes in the last decade to 1.6 million, they argue there are votes to be won by any party that promises radical change.

Danielle Morey, 28, who rents privately in Portsmouth with her partner, Mikey, and two young children, told the Guardian she was watching the manifestos closely. She has lived in nine different homes in the last decade and her four-year-old son has known four different bedrooms, as they have moved out because of problems such as mould or been evicted through no fault of their own. Her problems with living conditions are common. A quarter of rented homes are in such disrepair they are classed as “non-decent”. Morey’s family were turfed out of their last property with less than a week’s notice and were left to move home in the snow.

“I am really interested in what the parties say on social housing,” she said. “We have been looking at who to vote for, but it seems hardly anyone is interested in getting younger families into affordable housing, and I mean actually affordable [that is cheaper than 80% of market rent, which is a common definition of affordable].”

The chief executive of Crisis, Jon Sparkes, said: “We constantly hear how the severe lack of affordable homes is leaving families going without food, missing bill payments and ultimately, being pushed into homelessness.

“We need to see action if we are to prevent thousands of people from losing their homes. The next government cannot ignore the widespread public desire to change the system.”

Campaign groups including Shelter and Generation Rent, as well as the growing tenants’ union movement, are also calling for the parties to commit to reforms of the private rental market, including scrapping section 21 “no fault” evictions which increase uncertainty for renters.

Evictions by private landlords are a leading cause of homelessness. Twenty-seven percent of households in housing need in England cited loss of private sector tenancy as a reason for homelessness, according to ONS data. Councils spent £1.1bn on temporary accommodation for homeless households between April 2018 and March 2019, according to Shelter. This has increased by 78% in the last five years.

New polling by Shelter suggests public support for more secure tenancies, which have been floated by both the Conservatives and Labour. Seventy percent of renting families with children told YouGov the next government should introduce indefinite tenancies, but 64% cautioned that politicians still cared more about landlords than renters.